Solving a Ski Slope: Length & Time for Descent

In summary, a skier starts gliding at 3m/s on horizontal frictionless snow and then goes down a 10 degree incline, reaching a speed of 15m/s at the bottom. To find the length of the incline and the time it takes to reach the bottom, we use the equation V^2=Vo^2 +2ax and split gravity into its components. The acceleration is found to be 9.8*sin(10) and the length of the incline can be calculated using this value.
  • #1
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Homework Statement


A skier is gliding along at 3m/s on horizontal frictionless snow. He suddenly starts down a 10 degree incline. His speed at the bottom is 15 m/s.
a) what is the length of the incline?
b) how long does it take for him to reach the bottom?
we know:
Vo=3m/s
Vf=15m/s
t=?
x=?
a=?

Homework Equations


V^2=Vo^2 +2ax



The Attempt at a Solution


i need help to find what the a is...and why it is that.
 
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  • #2
the only force acting on the skier is gravity but since the skier is going down a 10 degree incline gravity is giving him some acceleration but not 100% of it's full foce.

draw the Free Body Diagram and split up gravity into it's components where the acceleration will be parallel to the incline.
 
  • #3
okay from my freebody diagram i get sin(10)=9.8/a
a=56.4
and that is wrong...if anyone could explain to me how to do it properly please...id greatly appreciate it because i have my exam very soon.
 
  • #4
it should be 9.8*sin(10). the force acting parallel to the inclined plane is mgsin(theta).
 

FAQ: Solving a Ski Slope: Length & Time for Descent

What is the formula for calculating the length of a ski slope?

The formula for calculating the length of a ski slope is L = (V^2 * sin(2θ)) / g, where L is the length of the slope, V is the initial velocity, θ is the angle of the slope, and g is the acceleration due to gravity.

How do I determine the time it takes to descend a ski slope?

The time it takes to descend a ski slope can be calculated using the formula T = 2V * sin(θ) / g, where T is the time, V is the initial velocity, θ is the angle of the slope, and g is the acceleration due to gravity.

Can the length and time for descent of a ski slope be affected by external factors?

Yes, external factors such as wind, snow conditions, and the shape of the slope can affect the length and time for descent of a ski slope. These factors can either increase or decrease the length and time.

How can I improve my speed and time while skiing down a slope?

To improve your speed and time while skiing down a slope, you can try adjusting your body position, reducing friction by waxing your skis, and practicing proper turning techniques.

Why is it important to calculate the length and time for descent of a ski slope?

Calculating the length and time for descent of a ski slope is important for safety purposes. It allows skiers to properly plan their route and anticipate any potential hazards or challenges on the slope. It also helps to determine the level of difficulty of a slope and ensure that skiers are adequately prepared for it.

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